PSV Eindhoven, held 2-2 by Vitesse Arnhem on Saturday, are top with 47 points, three ahead of Ajax Amsterdam, who drew 1-1 against Roda JC Kerkrade, and Feyenoord.
"Normally I don't consider my young team as candidates for the title as we still have to improve a lot seeing today's match," Feyenoord coach Ronald Koeman said.
"But if the favourites keep dropping points we will stay in touch with the top."
Graziano Pelle set up 18-year-old Boetius after 24 minutes and he scored from just outside the box with a superb curled shot.
Roy Beerens equalised from close range after 63 minutes but Alkmaar were reduced to 10 men shortly afterwards when Nick Viergever was sent off for a rash tackle.
Dutch international Jordy Clasie restored the lead for Feyenoord and in stoppage time 18-year old Vilhena sealed the match on the counter attack.
Ajax Amsterdam missed the chance to reduce the gap on leaders PSV to one point and had to come from behind as Adil Ramzi punished hesitating defensive work from the home side six minutes before the interval.
Isaac Cuenca, on loan from Barcelona, connected with left back Daley Blind early in the second half to level the score.
Twente Enschede remain winless in 2013 after dropping their early lead from Dusan Tadic's 11th minute goal, against lowly PEC Zwolle.
A poor second half from Twente allowed Zwolle to equalise nine minutes from time through a penalty by Denni Avdic.